This paper studies the existence and the non-existence of global solutions to the initial boundary value problems for the non-linear wave equation The paper proves that every above-mentioned problem has a unique global solution under rather mild con"ning conditions, and arrives at some su$cient con
✦ LIBER ✦
Global Existence for a System of Non-Linear and Non-Local Transport Equations Describing the Dynamics of Dislocation Densities
✍ Scribed by Marco Cannone; Ahmad El Hajj; Régis Monneau; Francis Ribaud
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 340 KB
- Volume
- 196
- Category
- Article
- ISSN
- 0003-9527
No coin nor oath required. For personal study only.
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The proofs of Theorems 2 and 3 are very laborious and must be omitted. We merely mention that the proof of Theorem 2 is based on the definition of regular mapping, while the proof of Theorem 3 is based on Lemmas 6,7,17,18,and 19.
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We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchho! type in the whole space: , and '0, with initial data u(x, 0)"u (x) and u R (x, 0)"u (x).